Art is like that these days – available, reaching out, no longer content with sitting in quiet corners waiting for our epiphanies. Waiting is out, luring is in.

It is certainly working. Last Monday, 20,516 people visited the British Museum, and its annual figure is now at 6.03m, a step change from the 4.5m-5.5m visits of the past five years. Visits to national museums as a whole have risen about 16% over the past four years. Tate Modern had 100,000 visits over the Long Weekend and is running at 5.2m visitors a year. Other museums have had more spectacular leaps. The V&A jumped 138% in the five years to 2006, but this was primarily due to the ending of admission charges in 2001. Whatever the cause, the new reality is that art and heritage have taken on a central place in a leisure economy previously dominated by sport and Thorpe Park. In that role, for good or ill, art finds itself playing by different rules…

The metaphysics of art do not inhabit the contemporary vernacular. We don’t know what it is because we haven’t got the language. The fourth plinth in Trafalgar Square makes the point. We can’t agree what to put on it, so we hand it over to a succession of artists. Currently, it has Thomas Schütte’s Model for a Hotel 2007, which looks feeble from a distance. The next one is being chosen from a shortlist, only one of which, Anish Kapoor’s Sky Plinth, makes any attempt to engage with the space and the plinth itself. Bob and Roberta Smith’s Make Art, Not War is so glib, I can’t actually believe it’s seriously being considered. Empty, the plinth attests to the metaphysical void once inhabited by art.

Down at the Science Museum, I can barely move for the giant baby buggies. This is where you go with children on a rainy bank holiday. It has everything: interactivity, weird stuff and gee-whizzery on a huge scale. It does it well. No wonder – the current director is Chris Rapley, one of the best scientists we have. At the moment, however, there is an oddity lurking on the first floor. This is Listening Post, a work of art more than science, by Mark Hansen and Ben Rubin. It consists of a wall of tiny dot-matrix screens, across which flow and shimmy fragments taken from internet chatrooms. The words are also spoken by a neutral voice. The work shifts through different themes and rhythms, giving it a symphonic aspect.

It is superb. The New York Times critic rightly said it suggested a chapel of the age of communication. It has two big problems, however. First, it is partly disturbing, suggesting loneliness and anxiety. Second, you need to sit there in the half-dark, quietly doing nothing, silent and still. That’s what I did and, in the midst of the buggy-infested Science Museum on a wet bank holiday Monday, I was – entirely and at last – alone.